When a magnet attracts a nail, it is an action of a field. However, wehen electrons move in a radio antenna, it is an action of a wave. At the quantum level, we often hear that an electromagnetic wave "consists" of real photons while a (static) field "consists" of virtual photons.

This question is to clarify the difference between the action of a field and the action of a wave. Because this concept applies to any field, the question is not specifically about electromagnetism, but about any field, e.g. gravity as well.

Consider that a source of the field relatively slowly passes by a test object thus applying a force to it. The force however is not constant, but, say, periodic. One example would be a sea tide caused by the Moon rotating around the Earth.

Is the sea tide a result of the gravitational field of the Moon or a result of the gravitational wave generated by the Moon's rotation around the Earth? Clearly the former, as otherwise detecting gravitational waves would be too easy.

Would the answer change if hypothetically the Moon were circling around the Earth much faster (e.g. like a binary neutron star)? Generally, when we detect an action, how can we tell if it is from a field or from a wave?